33S NMR: Recent Advances and Applications

The purpose of this review is to present advances and applications of 33S NMR, which is an underutilized NMR spectroscopy. Experimental NMR aspects in solution, chemical shift tendencies, and quadrupolar relaxation parameters will be briefly summarized. Emphasis will be given to advances and applications in the emerging fields of solid-state and DFT computations of 33S NMR parameters. The majority of the examples were taken from the last twenty years and were selected on the basis of their importance to provide structural, electronic, and dynamic information that is difficult to obtain by other techniques.


Introduction
Sulfur is a widely distributed element in organic, inorganic, polymeric, industrial, and biological systems.It is the 16th most abundant element in the crust of the earth by mass and, thus, an essential component of minerals.Sulfur is transported, with a variety of oxidation states from −2 to +6, by fluids and melts during a wide range of geological processes.Among the four sulfur stable isotopes ( 32 S, 94.8%; 34 S, 4.37%; 33 S, 0.76%; and 36 S, 0.02%), only 33 S possesses a nuclear spin and, thus, is NMR active.Compared to 1 H, 13 C, 15 N, 31 P, and 19 F NMR, however, 33 S has received little attention since it suffers from low natural abundance (0.76%, Table 1), a low gyromagnetic ratio (2.055685 × 10 −7 rad T −1 s −1 ), and extremely low absolute sensitivity relative to that of protons (1.72 × 10 −5 ) [1][2][3][4][5].Furthermore, 33 S is quadrupolar in nature, with a spin quantum number of I = 3/2 and a relatively large nuclear quadrupole moment of −0.0678 × 10 −28 m 2 .As a result, the interaction between the nuclear quadrupole moment and the electric field gradient at the nucleus provides very effective relaxation mechanisms and, thus, broad linewidths in solution and significant anisotropic broadening of powder line shapes in the solid state.
Recent developments in instrumentation, new pulse sequences and methodologies, especially in the solid state, the large chemical shift range, and the availability of elemental 33 S (99.8 atom%) as the starting material for 33 S enrichment have alleviated some of the experimental difficulties.In addition, due to the widespread application of DFT calculations of NMR parameters, an increased use of 33 S NMR can be foreseen.General features and available experimental data for 33 S NMR spectroscopy are discussed in a number of earlier comprehensive reviews and compilations.As an example, Barbarella [2] summarized a wide range of applications up to 1992, while Musio [3] published a very comprehensive review that covers all aspects of 33 S NMR, including experimental conditions, the theoretical background of various NMR parameters, and a wide range of applications up to 2008.
In the present review, we have attempted to treat both experimental aspects and the theoretical background of 33 S parameters and a wide range of applications, with particular emphasis on the solid state and computational DFT methods.Most examples are selected from publications in the last 20 years, yet some older but classic 33 S NMR papers will also be discussed.An attempt will also be made to define areas where 33 S NMR could provide atomic structural information that is difficult to obtain using other techniques.

Revision of Nuclear Properties
Makulski [6] reinvestigated several nuclear dipole moments and magnetic shielding constants, including those of 33 S, using 3 He atoms in mixtures with gas molecules of nuclei under investigation.The SF 6 gas, in the pressure range of 5-25 atm, resulted in very narrow 33 S signals (∆ν 1/2 ~1 Hz), due to the zero electric field gradient on the sulfur nuclei, with a well-defined 1 J( 33 S, 19 F) = 250.91Hz (Figure 1).The 3 He and 33 S NMR frequencies showed linear density dependencies (Figure 2), which, upon extrapolation to the zero-pressure limit, resulted in a 33 S nuclear magnetic moment in terms of µ( 3 He).Since the experimental µ( 3 He) is known to have high accuracy, the resulting µ( 33 S) = 0.6432555 (10)µ N is more accurate by an order of magnitude than those previously reported [7,8] (Table 1).   3 He and 33 S NMR frequencies of the gaseous mixture 3 He, SF6 as a function of density [6].

33 S Enrichment
The stringent requirements in 33 S NMR studies, at natural abundance, are the extensive signal averaging and the high concentrations needed for a successful spectrum.In most cases, especially for biologically relevant low concentrations, the use of [ 33 S]-labeled compounds is necessary.The synthesis of labeled compounds usually involves typical inorganic and organic reactions using, in most cases, elemental 33 S (99.8 atom%) as the Figure 2. 3 He and 33 S NMR frequencies of the gaseous mixture 3 He, SF 6 as a function of density [6].

33 S Enrichment
The stringent requirements in 33 S NMR studies, at natural abundance, are the extensive signal averaging and the high concentrations needed for a successful spectrum.In most cases, especially for biologically relevant low concentrations, the use of [ 33 S]-labeled compounds is necessary.The synthesis of labeled compounds usually involves typical inorganic and organic reactions using, in most cases, elemental 33 S (99.8 atom%) as the starting material.A typical example is the synthesis of [ 33 S]-taurine, which was achieved according to Scheme 1: disulfide ions, 33 S 2− 2 , which were prepared by the reaction of elemental 33 S (99.8 atom%) with NaOH in the presence of hydrazine, reacted with 2-(Boc-amino) ethyl bromide to produce [ 33 S 2 ]-dissulfide.Treatment with performing acid produced [ 33 S]taurine [9].[ 33 S 2 ]-L-cystine was also prepared with a similar synthetic root [10].Literature procedures were also used for the synthesis of [ 33 S]-diphenyl disulfide and its precursor, thiophenol [11].
The 33 S NMR spectrum of 0.1 mM [ 33 S]-taurine in D 2 O (δ = −6.7 ppm, ∆ν 1/2 = 11.5 Hz), at 14.1 T (see Figure 3), shows a reasonable signal with S/N = 9, using 4 × 10 4 scans and a total experimental time of ~10.4 h.Taking into consideration that T 1 ≈ 51 ms, the pulse repetition time, T p , could be as short as T p = 4T 1 ≈ 250 ms; thus, the total experimental time can be reduced by a factor of ~3.7.In humans, the concentrations of taurine are in the range of 10 to 100 µM in plasma and 10 to 70 µM in skeletal muscles and the heart; 33 S-labeled taurine, therefore, can be detected in metabolic and pharmacokinetic studies.
The 33 S NMR spectrum of 0.1 mM [ 33 S]-taurine in D2O (δ = −6.7 ppm, Δν1/2 = 11.5 Hz), at 14.1 T (see Figure 3), shows a reasonable signal with S/N = 9, using 4 × 10 4 scans and a total experimental time of ~10.4 h.Taking into consideration that T1 ≈ 51 ms, the pulse repetition time, Τp, could be as short as Τp = 4T1 ≈ 250 ms; thus, the total experimental time can be reduced by a factor of ~3.7.In humans, the concentrations of taurine are in the range of 10 to 100 µM in plasma and 10 to 70 µM in skeletal muscles and the heart; 33 Slabeled taurine, therefore, can be detected in metabolic and pharmacokinetic studies.S]-taurine in D2O, acquisition parameters: spectral width = 250 ppm, acquisition time = 0.284 s, pulse delay = 0.65 s, number of scans = 40,000.The FID data were multiplied by a 2 Hz exponential line broadening factor prior to Fourier transformation.Adopted with permission from [9].Copyright 2023, John Wiley & Sons Ltd.The chemical shift range has been corrected relative to saturated (NH4)2SO4 in D2O (0 ppm), according to IUPAC recommendation [5].

Ultra-High Magnetic Fields and High Sensitivity Detection Schemes
The use of ultra-high magnetic fields has significantly increased the sensitivity of 33 S NMR, in addition to increasing signal dispersion in the case of more complicated systems.The use of ultra-high field instrumentation is also most advantageous in the case of: (a) large molecular weight systems in solution, outside the extreme narrowing condition, The FID data were multiplied by a 2 Hz exponential line broadening factor prior to Fourier transformation.Adopted with permission from [9].Copyright 2023, John Wiley & Sons Ltd.The chemical shift range has been corrected relative to saturated (NH 4 ) 2 SO 4 in D 2 O (0 ppm), according to IUPAC recommendation [5].

Experimental NMR Aspects of Liquid Samples 4.1. Ultra-High Magnetic Fields and High Sensitivity Detection Schemes
The use of ultra-high magnetic fields has significantly increased the sensitivity of 33 S NMR, in addition to increasing signal dispersion in the case of more complicated systems.The use of ultra-high field instrumentation is also most advantageous in the case of: (a) large molecular weight systems in solution, outside the extreme narrowing condition, since the m = ½ → m = −1/2 component will dominate the spectrum and it is significantly narrower than the other component (see below on quadrupolar relaxation); and (b) in the solid state since the second-order quadrupolar linewidth of the m = ½ → m = −1/2 decreases linearly with the magnetic field B o (see Section on Solid State).
A 10 mm 33 S cryogenic probe with an inner RF coil in the temperature range of 9-12 K was described as having a 3.5-fold increase in sensitivity relative to that of a conventional 5 mm broadband probe [12].A further improvement in sensitivity was achieved with a preamplifier and switch that were cooled to 60 K by a cold helium gas [13].The quality factor Q of the rf coil was increased to 271 compared to 54 at room temperature.Figure 4 shows a comparison of the 33 S NMR sensitivity using: (a) the conventional 5 mm broadband probe; (b) the 10 mm cryoprobe at room temperature; and (c) the 10 mm cryoprobe with a cold switch and preamplifier.The achievable sensitivity enhancement of ~9.8 in (c) provides a technique to investigate biologically important samples at low mM concentrations for 33 S nuclei in highly symmetric environments.

Optimization of Experimental Parameters-Effects of Low-Viscosity Solvents and Temperature
In the case of a non-symmetric electronic environment around the 33 S nucleus, the extremely short quadrupolar relaxation times result in extensive line broadening and, thus, a reduction in the S/N ratio.Sensitivity, however, should be evaluated relative to the achievable S/N ratio in a given period of time.For the broad 33 S resonance, T 1 = T 2 , thus significantly short pulse repetition times of ~4T 2 can be used.This results in an S/N ratio per unit time that is practically independent of T 2 and, thus, resonance linewidth (see below on the effect of acoustic ringing on the achievable S/N ratio).
Increasing the temperature and/or dilution of high-viscosity liquids with low viscosity solvents can reduce the linewidth of 33 S. For moderate dilution, an optimum balance in resolution vs. S/N ratio can be achieved [14].Further reductions in linewidths can be achieved with the use of supercritical solvents, which combine fluid densities with gas-like viscosities.Unfortunately, despite some original optimism, the resolution advantages were significantly inferior to those expected on the basis of the viscosities of supercritical solvents [2].Thus, no further applications have so far been reported.[13].The quality factor Q of the rf coil was increased to 271 compared to 54 at room temperature.Figure 4 shows a comparison of the 33 S NMR sensitivity using: (a) the conventional 5 mm broadband probe; (b) the 10 mm cryoprobe at room temperature; and (c) the 10 mm cryoprobe with a cold switch and preamplifier.The achievable sensitivity enhancement of ~9.8 in (c) provides a technique to investigate biologically important samples at low mM concentrations for 33 S nuclei in highly symmetric environments.Acquisition parameters were: spectral width 130 ppm; acquisition time 0.1 s; preacquisition delay 6-10 µs; relaxation delay 0.05 s; number of scans 40,000 (the corresponding experimental time was 2 h).The NMR spectra were obtained: (a) using a conventional 5 mm broadband probe, T = 300 K; (b) with the 10 mm cryogenic probe with a room temperature rf switch and a preamplifier, T = 300 K; (c) using the 10 mm cryogenic probe with a cold rf switch and a cold preamplifier operated at 60 K.The sample temperature was 292 K. Reprinted with permission from [13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.Acquisition parameters were: spectral width 130 ppm; acquisition time 0.1 s; preacquisition delay 6-10 µs; relaxation delay 0.05 s; number of scans 40,000 (the corresponding experimental time was 2 h).The NMR spectra were obtained: (a) using a conventional 5 mm broadband probe, T = 300 K; (b) with the 10 mm cryogenic probe with a room temperature rf switch and a preamplifier, T = 300 K; (c) using the 10 mm cryogenic probe with a cold rf switch and a cold preamplifier operated at 60 K.The sample temperature was 292 K. Reprinted with permission from [13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

Acoustic Ringing
Observation of broad resonances of low natural abundance, low frequency, and sensitivity in quadrupolar nuclei is very problematic due to rolling baseline artifacts.They were attributed to ultrasonic waves from the effect of the rf.pulses and are often referred to as acoustic ringing [14,15].The most commonly used method to alleviate the problem is the use of a preacquisition delay, ∆t, which inevitably results in a significant reduction in the S/N ratio by a factor of exp(−∆t/T 2 ).Thus, resonances with linewidths greater than 4-5 kHz are virtually lost.The most efficient methods for recording very broad resonances are the use of multipulse sequences such as the RIDE and extended spin-echo sequences, which can be routinely applied without any hardware or probe modification [14,15].More recently, an interactive baseline correction algorithm for solid-state NMR spectra was reported [16].The method, which can also be applied to liquid states, does not make any hypothesis regarding the NMR line shapes and does not modify the recorded FID data points.

Magnetization Transfer Experiments-2D Inverse Detection
Inverse detection schemes in which polarization is transferred from 1 H to the X nucleus through n J( 1 H,X) couplings and then back to 1 H for detection have proved extremely useful for the I = 1/2 nuclei.In the case of 33 S, inverse detection was possible only in high-symmetric systems with a zero electric field gradient.Jackowski et al. [17] investigated intermolecular interactions on 33 S chemical shifts of gaseous SF 6 and its binary complexes with Xe, CO 2, and NH 3 at 298 K with the use of a refocused 19 F-33 S heteronuclear multiple-quantum coherence NMR.This polarization transfer experiment from 19 F to 33 S permitted the indirect detection of 33 S even in low-density samples (Figure 5).This allowed investigation of the density dependence of δ( 33 S) and 1 J( 19 F-33 S).Similarly, 19 F- 33 S HMBC experiments were used to investigate SF 6 dissolved in thermotropic liquid crystals [18].

Referencing Techniques
For 33 S NMR, as is common with several heteronuclei, a variety of reference compounds and referencing procedures, both internal and external, have been suggested.There are two adopted scales of 33 S NMR chemical shifts, namely the one based on neat carbon disulfide, CS2, and the other one-on saturated (NH4)2SO4 in D2O.The 33 S NMR signals of both standards are relatively sharp, with the former being noticeably broader because of increased electronic asymmetry around the nucleus, which is illustrated in Figure 6.Despite the IUPAC recommendation of the use of saturated (NH4)2SO4 in D2O as a reference compound [5], Cs2SO4, Na2SO4, and other sulfates have also been utilized.The SO chemical shift was shown to be dependent on concentration, nature of counterion, pH, and temperature.As discussed in detail in [3], the reported chemical shift variations are not significant compared to the accuracy of recording very broad 33 S resonances.Several authors also still use CS2 as a reference.The conversion of the SO and the CS2 scales was reported to be [3]: For diamagnetic solutions, the double tube method was used with the reference compound in the inner tube or capillary, without any susceptibility correction, since it is expected to be much smaller than the accuracy of the measurement of the chemical shift.It  19 F NMR correlation spectrum of gaseous SF 6 at high pressure (approximately 20 atm).The 2D spectrum was obtained by the application of the refocused 33 S-19 F HMQC technique.Sixteen scans were collected for each TPPI dataset in 180 t 1 increments.The maximum t 1 and t 2 times were 90 and 512 ms, respectively.A relaxation delay of 0.1 s was used.The data matrix containing 180 × 2048 complex points in t 1 and t 2 was zero-filled to 512 × 4096 complex points and apodized by a cosine function in both time domains prior to Fourier transformation.Reprinted with permission from [17].Copyright 2002, The American Institute of Physics, Melville, NY, USA.

Referencing Techniques
For 33 S NMR, as is common with several heteronuclei, a variety of reference compounds and referencing procedures, both internal and external, have been suggested.There are two adopted scales of 33 S NMR chemical shifts, namely the one based on neat carbon disulfide, CS 2 , and the other one-on saturated (NH 4 ) 2 SO 4 in D 2 O.The 33 S NMR signals of both standards are relatively sharp, with the former being noticeably broader because of increased electronic asymmetry around the nucleus, which is illustrated in Figure 6.Despite the IUPAC recommendation of the use of saturated (NH 4 ) 2 SO 4 in D 2 O as a reference compound [5], Cs 2 SO 4 , Na 2 SO 4 , and other sulfates have also been utilized.The SO 2 − 4 chemical shift was shown to be dependent on concentration, nature of counterion, pH, and temperature.As discussed in detail in [3], the reported chemical shift variations are not significant compared to the accuracy of recording very broad 33 S resonances.Several authors also still use CS 2 as a reference.The conversion of the SO 2 − 4 and the CS 2 scales was reported to be [3]: For diamagnetic solutions, the double tube method was used with the reference compound in the inner tube or capillary, without any susceptibility correction, since it is expected to be much smaller than the accuracy of the measurement of the chemical shift.It should be emphasized, however, that due to the high B 0 stability of modern NMR instrumentation, the spectrum of the reference compound can be recorded in a separate experiment (when unlocked) with the chemical shift calculated at 0 ppm.For the study of paramagnetic solutions, the use of a cylindrical and a spherical tube has been proposed [14,19].The 33 S resonance of the reference compound is recorded in both cells; the bulk magnetic susceptibility correction is the chemical shift difference of the two measurements.
Recently, Jackowski and Wilczek [20] recommended the use of helium-3 gas as a primary universal reference standard.Gas phase 3 He NMR measurements provided the resonance frequency of an isolated helium-3 atom, which is independent of temperature, and no rovibration correction is needed.In addition, very accurate shielding constant calculations of σ ref ( 3 He) are known [21].The shielding from 3 H to, e.g., 33 S can be obtained with the double resonance method using the 2 D NMR signal of the lock solvent; thus, no reference standard is needed.
Molecules 2024, 29, x FOR PEER REVIEW 9 of 43 [14,19].The 33 S resonance of the reference compound is recorded in both cells; the bulk magnetic susceptibility correction is the chemical shift difference of the two measurements.
Recently, Jackowski and Wilczek [20] recommended the use of helium-3 gas as a primary universal reference standard.Gas phase 3 He NMR measurements provided the resonance frequency of an isolated helium-3 atom, which is independent of temperature, and no rovibration correction is needed.In addition, very accurate shielding constant calculations of σref( 3 He) are known [21].The shielding from 3 H to, e.g., 33 S can be obtained with the double resonance method using the 2 D NMR signal of the lock solvent; thus, no reference standard is needed.

Experimental Chemical Shift Ranges
The 33 S NMR scale has a wide chemical shift range of over 1000 ppm, as illustrated in

Chemical Shifts Experimental Chemical Shift Ranges
The 33 S NMR scale has a wide chemical shift range of over 1000 ppm, as illustrated in Figure 7, which partly compensates for experimental difficulties in observing the NMR signals.The order of increasing deshielding follows the trend (with several exceptions): (i) singly bonded sulfur; (ii) multiply bonded sulfur; (iii) sulfur belonging to delocalized functional groups; and (iv) sulfur bonded to several oxygen atoms.Inorganic sulphides As noted above, the 33 S NMR linewidth is dependent on the magnitude of the electric field gradient at the sulfur nucleus, which in turn depends on the degree of symmetry around sulfur.Thus, while narrow lines are observed for compounds with high molecular symmetry, compounds with lower molecular symmetry, such as sulfoxides and sulfides, give much broader lines.Tables 2 and 3 contain experimental 33 S NMR chemical shifts and line widths of several representative sulfides, sulfoxides, and sulfones compiled from the reviews by Musio [3] (compounds 1-12, 28-33), Aliyev [22] (compounds 13-16), and the original paper by Ngassoum et al. [23] (compounds 17-27, 34-38).Most of the original experimental data (which were largely not included in those tables) were published in the early papers by different authors; see most representative reviews [1][2][3] and key original references given therein.  3S NMR chemical shift ranges of some of representative sulfur functional groups of diamagnetic organic and inorganic compounds relative to saturated (NH4)2SO4 in D2O as reference calibrated at 0 ppm.As noted above, the 33 S NMR linewidth is dependent on the magnitude of the electric field gradient at the sulfur nucleus, which in turn depends on the degree of symmetry around sulfur.Thus, while narrow lines are observed for compounds with high molecular symmetry, compounds with lower molecular symmetry, such as sulfoxides and sulfides, give much broader lines.Tables 2 and 3 contain experimental 33 S NMR chemical shifts and line widths of several representative sulfides, sulfoxides, and sulfones compiled from the reviews by Musio [3] (compounds 1-12, 28-33), Aliyev [22] (compounds 13-16), and the original paper by Ngassoum et al. [23] (compounds 17-27, 34-38).Most of the original experimental data (which were largely not included in those tables) were published in the early papers by different authors; see most representative reviews [1][2][3] and key original references given therein.
. 33 S NMR chemical shift ranges of some of representative sulfur functional groups of diamagnetic organic and inorganic compounds relative to saturated (NH4)2SO4 in D2O as reference calibrated at 0 ppm.
. 33 S NMR chemical shift ranges of some of representative sulfur functional groups of diamagnetic organic and inorganic compounds relative to saturated (NH4)2SO4 in D2O as reference calibrated at 0 ppm.a Chemical shifts are given in the SO4 2-and CS2 scales (the latter are given in parenthesis).a Chemical shifts are given in the SO4 2-and CS2 scales (the latter are given in parenthesis).It appears that δ( 33 S) is sensitive to the electronic effects of substituents, molecular conformation, ring strain, ionization state, temperature, solvent, and, in a few cases, concentration.Characteristic structural trends dealing with the ring strain of cyclic sulfides, sulfoxides, and sulfones were explicitly formulated by Musio [3].By comparing dimethyl derivatives and the corresponding thiiranes, significant shielding is observed upon It appears that δ( 33 S) is sensitive to the electronic effects of substituents, molecular conformation, ring strain, ionization state, temperature, solvent, and, in a few cases, concentration.Characteristic structural trends dealing with the ring strain of cyclic sulfides, sulfoxides, and sulfones were explicitly formulated by Musio [3].By comparing dimethyl derivatives and the corresponding thiiranes, significant shielding is observed upon It appears that δ( 33 S) is sensitive to the electronic effects of substituents, molecular conformation, ring strain, ionization state, temperature, solvent, and, in a few cases, concentration.Characteristic structural trends dealing with the ring strain of cyclic sulfides, sulfoxides, and sulfones were explicitly formulated by Musio [3].By comparing dimethyl derivatives and the corresponding thiiranes, significant shielding is observed upon It appears that δ( 33 S) is sensitive to the electronic effects of substituents, molecular conformation, ring strain, ionization state, temperature, solvent, and, in a few cases, concentration.Characteristic structural trends dealing with the ring strain of cyclic sulfides, sulfoxides, and sulfones were explicitly formulated by Musio [3].By comparing dimethyl derivatives and the corresponding thiiranes, significant shielding is observed upon cyclization due to the influence of ring strain tension (−145 ppm for thiirane, −205 ppm for thiirane 1-oxide, and −75 ppm for thiirane 1,1-dioxide).Three-membered ring compounds are markedly more shielded than larger rings.On going from three-to four-membered rings, a significant deshielding is observed; from four-to five-membered rings, a further deshielding is observed only in the case of sulphonyl compounds. 33S is more shielded in six-membered rings than in five-membered rings by approximately 40-50 ppm, and, thus, it occurs in the same range as the open-chain compounds.This can be attributed to the geometric stability of six-membered rings and the absence of ring-strain interactions.
Several empirical correlations have been reported, which have been analyzed in detail in the comprehensive review of Musio [3].Thus, only a brief account will be given below.A linear correlation between δ( 33 S) of sulphonates, RSO − 3 , and δ( 33 C) of carboxylates, RCOO − , was obtained in the form which shows that δ( 33 S) is two times more sensitive to substituent effects than that of δ( 13 C).Good linear correlations between δ( 33 S) and Taft polar substituent constant σ* were obtained for symmetric dialkyl sulphones of the form and monosubstituted dimethyl sulfones of the form In the last fifteen years, there has been no significant research activity on empirical correlations, presumably due to the fact that theoretical calculations of 33 S chemical shifts can provide accurate results and, thus, important information on electron distribution and bonding properties (see Section on Computations).

Relaxation in the Extreme Narrowing Condition
In the absence of chemical exchange, the linewidth of quadrupolar nuclei in isotropic systems is given by where T 1 and T 2 are the longitudinal and transverse relaxation times, respectively, C Q is the nuclear quadrupolar coupling constant (NQCC) defined as where Q is the nuclear electric quadrupole moment, q zz is the largest component of the electric field gradient tensor at the 33 S nucleus, e is the charge of the electron, n Q is the asymmetric parameter given by and τ c is the correlation time, which for spherical molecules is given by the Stokes-Debye formula.
where r is the radius of the molecule, n v is the viscosity of the solution, K B -the Boltzmann factor, and T-the absolute temperature.Narrow resonances can be expected for small molecular weight molecules and C Q values at elevated temperatures and low viscosity values. 33S NMR signals of a few Hz can only be observed in highly symmetric electronic environments around the sulfur nucleus, such as SO 2 − 4 anions.The product ) can be obtained from 33 S relaxation times when the correlation time can be estimated through Equation (8).More precise values of τ c can be obtained from relaxation time measurements of other nuclei, such as 13 C and 2 D, denoted as the dual spin probe method.Thus, the 33 S NQCCs of the C 6 H 4 SO − 3 (0.5 MHz) and 3-NH + 3 C 6 H 4 SO − 3 (1.0MHz) anions were determined with the combined use of 33 S linewidths, 13 C T 1 relaxation times, and NOE measurements [24].The 33 S NQCCs of (CH 3 ) 2 SO 2 (1.8 MHz) and CS 2 (13.8 MHz) were measured in liquid crystalline solvents [25].The order parameters were obtained from 1 H NMR spectra for (CH 3 ) 2 SO 2 and 13 C chemical shifts for CS 2 .Information on the NQCC of (CH 3 ) 2 SO 2 in chloroform solution was also obtained (1.63 MHz for n Q = 0 and 1.41 MHz for n Q = 1) with the combined use of 33 S and 2 D T 1 relaxation time measurements.The values in chloroform solution are lower than those reported for liquid crystalline solvents, presumably due to solvent effects and experimental errors [25].In the last twenty years, however, the great majority of 33 S NQCCs were obtained with solid-state and zero-field NMR techniques (see Section 8 on Solid State and Section 9 on Computations).

Relaxation Outside the Extreme Narrowing Condition
The decay of the longitudinal and transverse magnetization components outside the extreme narrowing condition, ω 0 τ c >> 1, is no longer exponential but a weighted sum of I + 1/2 = 2 exponentials.The NMR signal of the m = 1/2 → m = −1/2 component will dominate the spectrum because it is significantly narrower than the other component [26,27].This phenomenon has been successfully used in 17 O NMR to investigate ligand binding to proteins [14] or small MW molecules dissolved in highly viscous solvents [28].Unfortu-nately, no application of 33 S NMR has so far been reported in solution, contrary to the case in the solid state (see Section 8 on Solid State).

Selected Applications in Solution 7.1. Biological Applications
33 S was used to investigate the effect of the enzyme chondroitinase (ACII), a bacterial lyase that specifically digests chondroitin sulfate A (ChS-A), which is a sulfated glycosaminoglycan of over 100 residue disaccharides, each of which can be sulfated in variable positions and quantities [13].ChS-A, in the absence of ACII, shows no observable 33 S NMR signal due to extensive linewidth broadening.With an increase in the incubation time and, thus, enzymatic catalysis, a sharp peak at −0.5 ppm appeared (Figure 8).This was attributed to SO 2 − 4 species produced due to the enzymatic cleavage of the Nacetylhexosaminide linkage in ChS-A. 33S NMR was also utilized to investigate the tissue of the mantle edge, midgut, and adductor muscles of a scallop.SO 2 − 4 species were clearly identified relative to the taurine resonance (Figure 9).tained with the use of a 33 S cryogenic probe, a room-temperature rf switch, and a preamplifier.Acquisition parameters: spectral width 130 ppm; acquisition time 0 delay 10 µs; and relaxation delay 0.01 s.Total number of scans: 400,000, and exp h, 10 min.The sample temperature was in the range of 290-292 K. Reprinted wit [13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.   S cryogenic probe with a cold rf switch and a cold preamplifier (60 K).The acquisition parameters were the same as in Figure 8. 400,000 scans were recorded, and the experimental time was 16 h 10 min.Sample temperature: 291-292 K. Reprinted with permission from [13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

77 Se as a Substitution for Sulfur-1 H Detected 77 Se NMR in Proteins
77 Se enrichment of proteins has been used as a tool to expand the biological applications of NMR [29] based on the great sensitivity of 77 Se to electronic environments and dynamics [4].Recently, sulfur sites with double-labeled 13 C and 77 Se proteins were explored with the use of triple resonance 1 H-detected 77 Se NMR [30].For the case of double-labeled methionine, the coupling constants 1 J( 1 H, 13 C) = 125-140 Hz and 1 J( 13 C, 77 Se) = 60-70 Hz were used for coherence transfers as follows: 13 The great resolution and sensitivity advantages of the method are illustrated in Figure 10 using a concentration of 300 µM of the protein CUE (MW = 6 kDa), in which methionine residues were substituted to ~95% with double-labeled 13 CH 3 -77 Se-methionine.Although 1 H and 13 C chemical shift differences are very small, the 77 Se chemical shifts of the methionine residues M467 and M450 show a significant difference of 4.2 ppm.The technique requires specific hardware and decoupling schemes that are not, at present, commercially available.It remains to be seen what the advantages of the method are for proteins with molecular weights larger than 20 kDa since, at ultra-high magnetic fields, the line broadening might be significant due to the very large chemical shift anisotropy of 77 Se [4].
the methionine residues M467 and M450 show a significant difference of 4.2 ppm.The technique requires specific hardware and decoupling schemes that are not, at present, commercially available.It remains to be seen what the advantages of the method are for proteins with molecular weights larger than 20 kDa since, at ultra-high magnetic fields, the line broadening might be significant due to the very large chemical shift anisotropy of 77 Se [4].

Basic Considerations
33 S NMR can provide important information about molecular structure and dynamics in the solid state; however, the extremely broad powder patterns ranging from hundreds of kHz to tens of MHz due to large quadrupolar anisotropic interaction and the very long longitudinal relaxation hinder the routine application of this nucleus [1,31].Figure 11 shows the energy levels resulting from the Zeeman first-and second-order quadrupolar interactions for a nucleus with I = 3/2 [32].The first-order quadrupolar interaction does not affect the central transition.The satellite transitions are shifted by ±2ωQ, the exact amount of which is orientation-dependent.The second-order quadrupolar interaction moves the energy levels by equal and opposite amounts and strongly affects the satellite transitions 1/2 ↔ 3/2 and −3/2 ↔ −1/2, thus resulting in extremely broad resonances.
There are several methodologies that have been developed for the acquisition of 33 S NMR spectra in the solid state:  8. 33 S NMR in the Solid State 8.1.Basic Considerations 33 S NMR can provide important information about molecular structure and dynamics in the solid state; however, the extremely broad powder patterns ranging from hundreds of kHz to tens of MHz due to large quadrupolar anisotropic interaction and the very long longitudinal relaxation hinder the routine application of this nucleus [1,31].Figure 11 shows the energy levels resulting from the Zeeman first-and second-order quadrupolar interactions for a nucleus with I = 3/2 [32].The first-order quadrupolar interaction does not affect the central transition.The satellite transitions are shifted by ±2ω Q , the exact amount of which is orientation-dependent.The second-order quadrupolar interaction moves the energy levels by equal and opposite amounts and strongly affects the satellite transitions 1/2 ↔ 3/2 and −3/2 ↔ −1/2, thus resulting in extremely broad resonances.(iv) Indirectly detected satellite transition via saturation of the proton reservoir.
(v) Zero-field and frequency/field-swept solid-state NMR.
A synopsis of (i) to (v) will be given below.
For resonances broader than about 150 kHz, due to large CQ values, it is difficult to accurately record lineshapes with a single pulse technique.To overcome the problem, several approaches have been proposed to carry out spin-echo experiments of broad band excitation and refocusing at several frequencies to map out the lineshape [33].These approaches are time-consuming; nevertheless, Halat et al. [34] performed successful ultrawideline quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) 33 S NMR experiments at nat- There are several methodologies that have been developed for the acquisition of 33  (iv) Indirectly detected satellite transition via saturation of the proton reservoir.(v) Zero-field and frequency/field-swept solid-state NMR.
A synopsis of (i) to (v) will be given below.

Magic Angle Spinning Observation of the Central Transition: Effects of Bo and Population Transfer
The 1/2 ↔ −1/2 central transition of non-integer spins, such as 33 S, is not affected by first-order broadening.Consequently, the central transition appears as a relatively sharp peak at the center of the satellite transitions, which are often too broad to be detected.In several cases, however, the second-order effect of 33 S quadrupolar interactions contributes significantly to the line broadening of the central transition.MAS improves resolution but does not sufficiently remove anisotropic broadening.Thus, each distinct asymmetric 33 S electronic environment will give rise to a second-order quadrupolar power pattern under MAS, which can be several KHz wide, thus resulting in significant signal overlapping.The two main developments that have made 33 S solid-state NMR feasible are the availability of ultra-high magnetic field instruments and methods to enhance sensitivity via population transfer [35].
Second-order quadrupolar broadening, A, is inversely proportional to the strength of the static Bo field: For resonances broader than about 150 kHz, due to large C Q values, it is difficult to accurately record lineshapes with a single pulse technique.To overcome the problem, several approaches have been proposed to carry out spin-echo experiments of broad band excitation and refocusing at several frequencies to map out the lineshape [33].These approaches are time-consuming; nevertheless, Halat et al. [34] performed successful ultra-wideline quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) 33 S NMR experiments at natural abundance to investigate S 2 − sulfide and S 2 − 2 disulfide units of the Li-ion battery conversion of the NbS 3 electrode.Seventeen variable offset cumulative spectra were acquired at 20 T with a step size of 1970 ppm (128.5 KHz) in order to cover a spectral width of ~2.6 MHz.Spectral features corresponding to both S 2 − and S 2 − 2 with significantly different C Q values were identified and supported with DFT calculations (see Section 9 on Computations).

Magic Angle Spinning Observation of the Central Transition: Effects of B o and Population Transfer
The 1/2 ↔ −1/2 central transition of non-integer spins, such as 33 S, is not affected by first-order broadening.Consequently, the central transition appears as a relatively sharp peak at the center of the satellite transitions, which are often too broad to be detected.In several cases, however, the second-order effect of 33 S quadrupolar interactions contributes significantly to the line broadening of the central transition.MAS improves resolution but does not sufficiently remove anisotropic broadening.Thus, each distinct asymmetric 33 S electronic environment will give rise to a second-order quadrupolar power pattern under MAS, which can be several KHz wide, thus resulting in significant signal overlapping.The two main developments that have made 33 S solid-state NMR feasible are the availability of ultra-high magnetic field instruments and methods to enhance sensitivity via population transfer [35].
Second-order quadrupolar broadening, A, is inversely proportional to the strength of the static B o field: The 33 S linewidth, therefore, is expected to be significantly reduced with a concomitant enhancement in sensitivity.Figure 13 shows the significant advantages of recording the spectrum of KAl (SO 4 ) 2  Hansen et al. [37] reported significant sensitivity enhancements of 1.7 to 2.3 with the use of pairs of inversion pulses to induce selective polarization transfer between the four 33 S energy levels.The method was applied to surface ions and tetrathio metalates with quadrupolar nuclear parameter  values in the range of 0.3 to 1.2 MHz (Figure 14).The use of the WURST (wideband uniform rate smooth transaction) technique does not require a priori knowledge of the  and  values.Hansen et al. [37] reported significant sensitivity enhancements of 1.7 to 2.3 with the use of pairs of inversion pulses to induce selective polarization transfer between the four 33 S energy levels.The method was applied to surface ions and tetrathio metalates with quadrupolar nuclear parameter C Q values in the range of 0.3 to 1.2 MHz (Figure 14).The

Dynamic Nuclear Polarization (DNP) NMR
DNP has been extensively utilized to increase the sensitivity of NMR by several orders of magnitude and involves the transfer of polarization from highly polarized electron spins to nearby nuclear spins in the sample [38].Microwaves at a specific frequency cause transitions between coupled electron-nuclear spin states, resulting in nuclear spin polarization.Bellan et al. [39] performed the first 33 S DNP-NMR of ZnS nanoplatelets in order to characterize sulfur vacancies at the atomic scale.Figure 15A shows 33 S direct detection NMR spectra at 18.8 and 35.2 T with a total experimental time of 6 days 8 h and 6 h 20 min, respectively.Simulation of a single central transition resulted in δiso = −621 ppm,  = 5.2 MHz, and  = 0.40.On the contrary, the 67 Zn NMR showed the presence of three distinct central transitions due to the larger chemical shift range and, thus, sensitivity to the electronic environment.Application of the DNP method using a dipolar-mediated refocused INEPT technique (D-R INEPT) [40,41], in conjunction with QCPMG detection, resulted in a significant sensitivity enhancement by orders of magnitude of 33 S NMR, with a total experimental time of 6 h for the four subspectra (Figure 15B).The DNP-NMR spectrum was acquired at 105 K using the compound TEKPol as a polarizing agent at 9.4 T.

Dynamic Nuclear Polarization (DNP) NMR
DNP has been extensively utilized to increase the sensitivity of NMR by several orders of magnitude and involves the transfer of polarization from highly polarized electron spins to nearby nuclear spins in the sample [38].Microwaves at a specific frequency cause transitions between coupled electron-nuclear spin states, resulting in nuclear spin polarization.Bellan et al. [39] performed the first 33 S DNP-NMR of ZnS nanoplatelets in order to characterize sulfur vacancies at the atomic scale.Figure 15A shows 33 S direct detection NMR spectra at 18.8 and 35.2 T with a total experimental time of 6 days 8 h and 6 h 20 min, respectively.Simulation of a single central transition resulted in δ iso = −621 ppm, C Q = 5.2 MHz, and n Q = 0.40.On the contrary, the 67 Zn NMR showed the presence of three distinct central transitions due to the larger chemical shift range and, thus, sensitivity to the electronic environment.Application of the DNP method using a dipolar-mediated refocused INEPT technique (D-R INEPT) [40,41], in conjunction with QCPMG detection, resulted in a significant sensitivity enhancement by orders of magnitude of 33 S NMR, with a total experimental time of 6 h for the four subspectra (Figure 15B).The DNP-NMR spectrum was acquired at 105 K using the compound TEKPol as a polarizing agent at 9.4 T. Copyright 2023, The American Chemical Society, Washington, DC, USA.

Indirectly Detected Satellite Transition via Saturation of the Proton Reservoir
Satellite transitions result, in most cases, in extremely broad resonances that are typically invisible for the low-natural abundance nuclei, like 33 S. Recently, Frydman and collaborators introduced a novel method for enhancing satellite transitions that is based on the progressive saturation of the proton reservoir (PROSPR) in static solids [42].The PROSPR method includes a looped cross-polarization/spin diffusion process that progressively depletes the abundant 1 H polarization in solid samples.This 1 H depletion indirectly maps the NMR spectra of the heteronuclei as an attenuation of the abundant 1 H NMR signals.The achievable sensitivity enhancement with conventional NMR instruments and modest hardware modifications at room temperature is orders of magnitude greater in comparison to directly observed experiments [42].

Indirectly Detected Satellite Transition via Saturation of the Proton Reservoir
Satellite transitions result, in most cases, in extremely broad resonances that are typically invisible for the low-natural abundance nuclei, like 33 S. Recently, Frydman and collaborators introduced a novel method for enhancing satellite transitions that is based on the progressive saturation of the proton reservoir (PROSPR) in static solids [42].The PROSPR method includes a looped cross-polarization/spin diffusion process that progressively depletes the abundant 1 H polarization in solid samples.This 1 H depletion indirectly maps the NMR spectra of the heteronuclei as an attenuation of the abundant 1 H NMR signals.The achievable sensitivity enhancement with conventional NMR instruments and modest hardware modifications at room temperature is orders of magnitude greater in comparison to directly observed experiments [42].
Figure 16 illustrates the excellent sensitivity advantages of the PROSPR 33 S NMR spectrum of the ammonium sulfate (NH 4 ) 2 SO 4 ) in natural abundance.The PROSPR NMR patterns appear with increased line width, which can be attributed to the limited spectral selectivity of the cross-polarizing 33 S r.f.pulse.The use of an adiabatic demagnetization in the rotating frame (ADRF) cross-polarization scheme results in more effective multiple repeats and improved heteronuclei ( 33 S) spectral selectivity (Figure 16). Figure 16 illustrates the excellent sensitivity advantages of the PROSPR 33 S NMR spectrum of the ammonium sulfate (NH4)2SO4) in natural abundance.The PROSPR NMR patterns appear with increased line width, which can be attributed to the limited spectral selectivity of the cross-polarizing 33 S r.f.pulse.The use of an adiabatic demagnetization in the rotating frame (ADRF) cross-polarization scheme results in more effective multiple repeats and improved heteronuclei ( 33 S) spectral selectivity (Figure 16).

Zero-Field and Frequency-Swept NMR in the Solid State
In the case of organosulfur molecules or covalent bonds, as in the case of sulfur elements, the  values are reported to be more than 40 MHz.Thus, even with the highest currently available magnetic fields up to 28.8 T, the 33 S NMR spectra would only be detected with frequency-swept or field-swept solid-state methods [43].An alternative method, zero-field solid-state NMR or nuclear quadrupole resonance (NQR) spectroscopy, has been proposed, which utilizes the electric field gradient at the 33 S nucleus instead of an external magnetic field [43,44].Figure 17 shows an excellent zero-field 33 S NMR spectrum of 33 S-enriched dibenzyl disulfide, with  = 46.8MHz and  = 0.48 [7], which was recorded with a total experimental time of only 1 min [45].The method does not provide chemical shifts; however, the  and  parameters strongly depend on the local electric field gradient tensor on the sulfur nucleus and, thus, are very important structural parameters at the atomic level.

Zero-Field and Frequency-Swept NMR in the Solid State
In the case of organosulfur molecules or covalent bonds, as in the case of sulfur elements, the C Q values are reported to be more than 40 MHz.Thus, even with the highest currently available magnetic fields up to 28.8 T, the 33 S NMR spectra would only be detected with frequency-swept or field-swept solid-state methods [43].An alternative method, zero-field solid-state NMR or nuclear quadrupole resonance (NQR) spectroscopy, has been proposed, which utilizes the electric field gradient at the 33 S nucleus instead of an external magnetic field [43,44].Figure 17 shows an excellent zero-field 33 S NMR spectrum of 33 S-enriched dibenzyl disulfide, with C Q = 46.8MHz and n Q = 0.48 [7], which was recorded with a total experimental time of only 1 min [45].The method does not provide chemical shifts; however, the C Q and n Q parameters strongly depend on the local electric field gradient tensor on the sulfur nucleus and, thus, are very important structural parameters at the atomic level.

Selected Applications in Transition Metal Complexes, Ferroelectric, and Ferromagnetic Materials
Jakobsen et al. [46] utilized the WURST inversion pulses of the two ±3/2 ↔ ±1/2 satellite transitions of the +1/2 ↔ −1/2 central transition, which resulted in an increase in the S/N ratio by a factor ≥ 2 [37] to investigate disordered tetrathio transition metal anions.The use of two MAS frequencies (5.0 and 10.0 KHz) at 14.1 T in combination with static QCPMG at 19.6 T allowed the analysis of complex spectra of disordered ReS anions at natural abundance.The nuclear quadrupolar parameters,  and  , the chemical shift anisotropy parameters, δani and ηani, and δiso of two different S sites of the four sulfur atoms in the ReS anion were determined (Table 4).It was concluded that the use of high MAS speed resulted in narrow second-order line shapes for the central transition and, thus, improved precision of the CSA parameters.Copyright 2019, Elsevier Inc., Amsterdam, the Netherlands.

Selected Applications in Transition Metal Complexes, Ferroelectric, and Ferromagnetic Materials
Jakobsen et al. [46] utilized the WURST inversion pulses of the two ±3/2 ↔ ±1/2 satellite transitions of the +1/2 ↔ −1/2 central transition, which resulted in an increase in the S/N ratio by a factor ≥ 2 [37] to investigate disordered tetrathio transition metal anions.The use of two MAS frequencies (5.0 and 10.0 KHz) at 14.1 T in combination with static QCPMG at 19.6 T allowed the analysis of complex spectra of disordered ReS anions at natural abundance.The nuclear quadrupolar parameters,  and  , the chemical shift anisotropy parameters, δani and ηani, and δiso of two different S sites of the four sulfur atoms in the ReS anion were determined (Table 4).It was concluded that the use of high MAS speed resulted in narrow second-order line shapes for the central transition and, thus, improved precision of the CSA parameters.S]-dibenzyl disulfide, acquired at T = 200 K. Hydrogen, lfur in white, grey, and yellow, respectively.Reprinted with permission from [45]., Elsevier Inc., Amsterdam, the Netherlands.

pplications in Transition Metal Complexes, Ferroelectric, and Materials
et al. [46] utilized the WURST inversion pulses of the two ±3/2 ↔ ±1/2 satns of the +1/2 ↔ −1/2 central transition, which resulted in an increase in the a factor ≥ 2 [37] to investigate disordered tetrathio transition metal anions.o MAS frequencies (5.0 and 10.0 KHz) at 14.1 T in combination with static .6T allowed the analysis of complex spectra of disordered ReS anions at dance.The nuclear quadrupolar parameters,  and  , the chemical shift rameters, δani and ηani, and δiso of two different S sites of the four sulfur atoms nion were determined (Table 4).It was concluded that the use of high MAS d in narrow second-order line shapes for the central transition and, thus, cision of the CSA parameters.
adrupole coupling ( and  ), chemical shift anisotropy parameters (δani and ηani) 2H5)4N][ReS4] determined from natural abundance WURST polarization transfer-en-S and 33 S static QCPMG NMR spectra.a Adopted with permission from [46].Copyvier, Inc. −1/2 central transition, which resulted in an increase in the S/N ratio by a factor ≥ 2 [37] to investigate disordered tetrathio transition metal anions.The use of two MAS frequencies (5.0 and 10.0 KHz) at 14.1 T in combination with static QCPMG at 19.6 T allowed the analysis of complex spectra of disordered ReS − 4 anions at natural abundance.The nuclear quadrupolar parameters, C Q and n Q , the chemical shift anisotropy parameters, δ ani and η ani , and δ iso of two different S sites of the four sulfur atoms in the ReS − 4 anion were determined (Table 4).It was concluded that the use of high MAS speed resulted in narrow second-order line shapes for the central transition and, thus, improved precision of the CSA parameters. 33S MAS NMR (at 18.8 T), XANES, and Raman spectroscopy were applied to investigate sulfur speciation in iron-free and iron-poor glasses and, more specifically, to quantify the relative concentrations of S 2− , S 6+ , and any intermediate oxidation states present in silicate glasses quenched from melts [47]. 33S NMR can be used to detect S 2− and S 6+ in isotopically enriched samples with concentrations down to ~300 µg/g and long acquisition times of 1-2 days.However, both species have not been recorded simultaneously, although XANES and Raman showed the coexistence of S 2− and S 6+ in the glass samples.It was concluded that 33 S NMR can be applied to very specific synthetic S-rich systems but not to Fe-bearing natural compositions.Frydman and collaborators [48] used the 33 S PROSPR method to investigate ammonium sulfate, which undergoes a phase transition from its paraelectric (PE) to ferroelectric (FE) phase at T c = 223.5 K.In the temperature range of 296-224 K, there is a monotonic increase in the C Q values from 0.58 MHz to 0.67 MHz.At T c = 223.5 K, the spectrum showed the coexistence of both the PE and FE phases (Figure 18).The satellite transitions (STs) are much more sensitive to temperature changes of C Q than central transitions (CTs) and, thus, are of great importance in investigating dynamic processes over a wide range of time scales.to CS2 (0 ppm). 33S MAS NMR (at 18.8 T), XANES, and Raman spectroscopy were applied to investigate sulfur speciation in iron-free and iron-poor glasses and, more specifically, to quantify the relative concentrations of S 2− , S 6+ , and any intermediate oxidation states present in silicate glasses quenched from melts [47]. 33S NMR can be used to detect S 2− and S 6+ in isotopically enriched samples with concentrations down to ~300 µg/g and long acquisition times of 1-2 days.However, both species have not been recorded simultaneously, although XANES and Raman showed the coexistence of S 2− and S 6+ in the glass samples.It was concluded that 33 S NMR can be applied to very specific synthetic S-rich systems but not to Febearing natural compositions.

III
Frydman and collaborators [48] used the 33 S PROSPR method to investigate ammonium sulfate, which undergoes a phase transition from its paraelectric (PE) to ferroelectric (FE) phase at Tc = 223.5 K.In the temperature range of 296-224 K, there is a monotonic increase in the CQ values from 0.58 MHz to 0.67 MHz.At Tc = 223.5 K, the spectrum showed the coexistence of both the PE and FE phases (Figure 18).The satellite transitions (STs) are much more sensitive to temperature changes of  than central transitions (CTs) and, thus, are of great importance in investigating dynamic processes over a wide range of time scales. 33S NMR measurements using 33     33 S resonance frequencies in these experiments.The structures shown in between (a) and (b) depict the changes presumed for the ammonium and sulfate (red/yellow balls) groups of (NH 4 ) 2 SO 4 , upon going from the paraelectric phase (PE, lower inset) to the ferroelectic phase (FE, upper inset).Reprinted with permission from [48].Copyright 2023, Elsevier, Inc., Amsterdam, Netherlands. 33S NMR measurements using 33 S-entiched ferromagnetic EuS were performed in the range of 1.3 to 4.2 K [49].The extrapolated NMR signal at T = 0 has a value of 12.73 MHz (≈39 kG).EuS displays T 1.71 behavior above 4.2 K and T 2 dependence below 4.2 K.

Computations of 33 S NMR Parameters
9.1.Computational 33 S NMR in the Gas and Liquid Phase Theoretical calculations of 33 S NMR parameters, including the computation of 33 S isotropic nuclear shieldings, spin-spin coupling constants involving the 33 S isotope, and 33 S nuclear quadrupole coupling constants, received reasonable attention; see review by Musio [3].This was mainly for two reasons: calculations could help in identifying and elucidating the structural properties of the sulfur-containing molecules and, on the other hand, provide important information on the electron distribution and bonding situation around the sulfur atom.However, quite a few papers deal with computational 33 S NMR, mainly due to the lack of experimental data used to benchmark such calculations.
Generally, for the heavy elements, the available methods for the prediction of NMR parameters based on the Schrödinger equation become insufficient.In this case, the average orbital velocities of electrons in the vicinity of nuclei are close to the speed of light, giving rise to so-called relativistic effects such as spin-orbit coupling, also known as zitterbewegung (Darwin term), and mass-velocity correction, which can essentially affect NMR spectroscopic parameters.In general, relativistic effects on the NMR parameters become noticeable for the atoms beginning with the third period of the Periodic Table; however, for sulfur, such effects are expected (but not yet documented) to be fairly negligible.In one of the early papers, Kupka and coworkers [50] reported DFT calculations of 33 S NMR chemical shifts supported by experimental Raman and NMR data for thiophene and 3-methylthiophene.The Raman spectra of liquid thiophene were re-examined, and the performance of a hybrid B3PW91 functional used in combination with Pople's basis set 6-311++G(d,p) was benchmarked at the ab initio restricted Hartree-Fock method.
In a much later paper by the same leading author [51], the 33 S nuclear isotropic shielding constants of 2-thiouracil were calculated at the B3LYP/aug-ccpVXZ and B3LYP/aug-cc-pCVXZ levels of theory.Figure 19 compares the convergence patterns of the 33 S isotropic shieldings for 2-thiouracil calculated at the B3LYP level with the aug-cc-pVXZ and augcc-pCVXZ basis sets.For the first family of basis sets, a considerable scatter of calculated values was observed, while a smooth convergence was found for the latter one.The same behavior was noticed when the Locally Dense Basis Set (LDBS) approach was employed.The change in estimated Complete Basis Set (CBS) values due to the LDBS approach was found to be about 10% of the CBS value when all atoms were described with the aug-cc-pVXZ or aug-cc-pCVXZ basis sets.
Bagno in his early paper [52] reported 33 S NMR chemical shifts of a wide series of organic and inorganic sulfur-containing compounds, calculated at the DFT-GIAO level using the 6-311++G(2d,2p) basis set.Theoretical values were found to be in good agreement with the available experiment, with a few exceptions (mostly those for the charged species); see Table 5.Seven years later, Chesnut and Quin [53] reported a number of sulfur chemical shieldings (σ, ppm) evaluated at the scaled correlation level, including density functional theory, B3LYP/6-311+G(nd,p)//B3LYP/6-311+G(d,p), and modified MP2/6-311+G(nd,p) estimated infinite order Møller-Plesset theory with n = 2, the latter abbreviated as EMPI.The results of the 33 S NMR chemical shieldings are exemplified in Table 6.Calculations spanned over the range of available sulfur shieldings showed an agreement with the experiment of about 3% of the whole shielding range (Figure 20).For the EMPI method, the authors used a particular mixture of RHF and MP2 approaches.In many cases, the Møller-Plesset series of corrections appeared to converge in a manner that allowed the infinite series to be summed, so that the EMPI shieldings could be represented by a particular combination of the RHF and MP2 contributions.The 33 S NMR chemical shifts for fluoride, chloride, and bromide of the trimethylsulfonium ion and the S-methyltetrahydrothiophenium ion, in addition to the corresponding free cations, were also calculated within the same scaled DFT and EMPI approaches [54].Experimental values were found to agree with the calculated values with the standard deviation of 35 ppm (3.5% of the shielding range) established in the previous paper [53] for a larger variety of sulfur compounds (Table 6).
Molecules 2024, 29, x FOR PEER REVIEW 26 of 43 . 33 S nuclear isotropic shielding constants of 2-thiouracil calculated at the (A)-B3LYP/augcc-pVXZ and B3LYP/aug-cc-pCVXZ levels of theory, and (B)-using the LDBS approach, where only the sulfur atom was described using either the aug-cc-pVXZ or aug-cc-pCVXZ while the 6-31G* basis set was applied on H, C, N, and O atoms [51].
Bagno in his early paper [52] reported 33 S NMR chemical shifts of a wide series of organic and inorganic sulfur-containing compounds, calculated at the DFT-GIAO level using the 6-311++G(2d,2p) basis set.Theoretical values were found to be in good agreement with the available experiment, with a few exceptions (mostly those for the charged species); see Table 5.Seven years later, Chesnut and Quin [53] reported a number of sulfur chemical shieldings (σ, ppm) evaluated at the scaled correlation level, including density functional theory, B3LYP/6-311+G(nd,p)//B3LYP/6-311+G(d,p), and modified MP2/6-311+G(nd,p) estimated infinite order Møller-Plesset theory with n = 2, the latter abbreviated as EMPI.The results of the 33 S NMR chemical shieldings are exemplified in Table 6.Calculations spanned over the range of available sulfur shieldings showed an agreement with the experiment of about 3% of the whole shielding range (Figure 20).For the EMPI method, the authors used a particular mixture of RHF and MP2 approaches.In many cases, the Møller-Plesset series of corrections appeared to converge in a manner that allowed the infinite series to be summed, so that the EMPI shieldings could be represented by a particular combination of the RHF and MP2 contributions.The 33 S NMR chemical shifts for fluoride, chloride, and bromide of the trimethylsulfonium ion and the S-methyltetrahydrothiophenium ion, in addition to the corresponding free cations, were also calculated within the same scaled DFT and EMPI approaches [54].Experimental values were found to agree with the calculated values with the standard deviation of 35 ppm (3.5% of the shielding range) established in the previous paper [53] for a larger variety of sulfur compounds (Table 6).  3S nuclear isotropic shielding constants of 2-thiouracil calculated at the (A)-B3LYP/augcc-pVXZ and B3LYP/aug-cc-pCVXZ levels of theory, and (B)-using the LDBS approach, where only the sulfur atom was described using either the aug-cc-pVXZ or aug-cc-pCVXZ while the 6-31G* basis set was applied on H, C, N, and O atoms [51].
Musio and Sciacovelli [55] calculated sulfur isotropic absolute shielding constants at the DFT level of theory (B3LYP/6-311++G(2d,p)) in the series of 2-substituted sodium ethanesulfonates, X-CH 2 -CH 2 -SO 3 Na (X = H, CH 3 , OH, SH, NH 2 , Cl, Br, NH 3 + ).The diamagnetic contribution to the sulfur shielding constant was found to be constant, so that the observed deshielding of the 33 S resonance induced by the electron-removing substituents could be primarily related to the variations of the paramagnetic contribution.It was also demonstrated that oxygen lone pairs and sulfur core 2p electrons could play an active role in determining the paramagnetic contribution to sulfur shielding.With regard to the linewidth variations, they could be ascribed primarily to changes in the nuclear quadrupole coupling constants.The same authors [56] calculated the 33 S nuclear quadrupole coupling constants of 3-and 4-substituted benzenesulphonates and related charged species (both cations and anions) in the gas phase and in solution.The inclusion of the solvent effect in the calculations was found to be mandatory to reproduce experimental data.The solvent effect on the sulfur electric field gradient was shown to be due to electrostatic interactions.It was also shown that solvent interactions annihilated the Coulomb effect of the charge of the substituent and that those interactions caused a redistribution of electron density around the sulfur nucleus.

Computational 33 S NMR in the Solid State
For computational 33 S NMR in the solid-state, the available software and computa tional methods, the lineshape analysis and simulation of experimental data, together with the first principles calculations of NMR parameters, are of utmost importance.Some prac tical observations gained from a wide application of those approaches include, first of all the choice of basis set and cluster approximation.Starting from a crystal structure, it is the accuracy of the unit cell parameters and atomic positions within the cell that determine the accuracy of calculated NMR parameters.The Gauge-Including Projector Augmented Wave (GIPAW) approach and its different modifications are particularly effective in re producing NMR parameters.Although these approaches were initially aimed at periodic systems, there have been adaptations that allow parameters to be calculated when there is some atomic disorder in solid solutions and even in glasses.In particular, for glasses Molecular Dynamics (MD) is effectively used to model the glass formation process, with the structural model further refined using DFT calculations, which then act as the inpu into GIPAW computation.For more details, see the recent review by Smith [31].
Wagler and coauthors [36] reported the solid-state 33 S MAS NMR spectra of a variety of inorganic sulfates recorded at magnetic fields ranging from 4.7 to 18.8 T and magic angle spinning (MAS) at the natural abundance of the 33 S isotope.A number of factor were considered when analyzing spectral linewidths, including magnetic field inhomoge neity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion, and quadru polar coupling.DFT calculations of the electric field gradient tensors revealed that the most significant contribution to the asymmetric electric field gradient around the sulfu nucleus was provided by the closest atoms, so that a general correlation could be observed

Computational 33 S NMR in the Solid State
For computational 33 S NMR in the solid-state, the available software and computational methods, the lineshape analysis and simulation of experimental data, together with the first principles calculations of NMR parameters, are of utmost importance.Some practical observations gained from a wide application of those approaches include, first of all, the choice of basis set and cluster approximation.Starting from a crystal structure, it is the accuracy of the unit cell parameters and atomic positions within the cell that determine the accuracy of calculated NMR parameters.The Gauge-Including Projector Augmented Wave (GIPAW) approach and its different modifications are particularly effective in reproducing NMR parameters.Although these approaches were initially aimed at periodic systems, there have been adaptations that allow parameters to be calculated when there is some atomic disorder in solid solutions and even in glasses.In particular, for glasses, Molecular Dynamics (MD) is effectively used to model the glass formation process, with the structural model further refined using DFT calculations, which then act as the input into GIPAW computation.For more details, see the recent review by Smith [31].
Wagler and coauthors [36] reported the solid-state 33 S MAS NMR spectra of a variety of inorganic sulfates recorded at magnetic fields ranging from 4.7 to 18.8 T and magic angle spinning (MAS) at the natural abundance of the 33 S isotope.A number of factors were considered when analyzing spectral linewidths, including magnetic field inhomogeneity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion, and quadrupolar coupling.DFT calculations of the electric field gradient tensors revealed that the most significant contribution to the asymmetric electric field gradient around the sulfur nucleus was provided by the closest atoms, so that a general correlation could be observed between calculated and experimentally determined nuclear electric quadrupolar coupling constants.
Sutrisno et al. [57] demonstrated that a series of layered transition metal disulfides display a wide range of 33 S quadrupole coupling constants and chemical shift anisotropy values.It was shown that the wide-line natural abundance solid-state NMR spectra of 33 S in a less symmetric environment could readily be obtained at the ultrahigh magnetic field of 21.1 T and that, surprisingly, these closely related materials displayed a wide range of 33 S quadrupole coupling constant and chemical shift anisotropy values, both experimental and calculated (Figure 21).
values.It was shown that the wide-line natural abundance solid-state NMR spectra o in a less symmetric environment could readily be obtained at the ultrahigh magnetic fi of 21.1 T and that, surprisingly, these closely related materials displayed a wide rang 33 S quadrupole coupling constant and chemical shift anisotropy values, both experime and calculated (Figure 21).Moudrakovski et al. [58] performed the assignment of various sites and the rela orientations of the electron field gradient (EFG) tensors by means of quantum chem calculations using the DFT method and Gauge Independent Atomic Orbitals (GIAO molecular clusters of about 100 to 120 atoms.CASTEP, a leading code for calculating properties of materials from first principles, was used, which is specifically designed periodic boundary conditions and a gauge-including projector-augmented wave pseu potential approach.Although only semiquantitative agreement was observed between experimental and calculated parameters, the calculations of 33 S QCPMG spectra for K2S and K2S2O8 (Figure 22) appeared to be very useful in the interpretation of the experime data.Moudrakovski et al. [58] performed the assignment of various sites and the relative orientations of the electron field gradient (EFG) tensors by means of quantum chemical calculations using the DFT method and Gauge Independent Atomic Orbitals (GIAO) on molecular clusters of about 100 to 120 atoms.CASTEP, a leading code for calculating the properties of materials from first principles, was used, which is specifically designed for periodic boundary conditions and a gauge-including projector-augmented wave pseudopotential approach.Although only semiquantitative agreement was observed between the experimental and calculated parameters, the calculations of 33 S QCPMG spectra for K 2 S 2 O 7 and K 2 S 2 O 8 (Figure 22) appeared to be very useful in the interpretation of the experimental data.
O'Dell and Ratcliffe [59] reported the crystal structure for taurine shown in Figure 23a.It was found that the most shielded component of the chemical shift anisotropy tensor, σ 33 , was aligned within 3 • of the S-C bond, with σ 11 pointing in the approximate direction of the S-O 2 bond, while the largest component of the EFG tensor, V 33 , was aligned very close to the S-O 1 bond (<5 • ), with V 22 pointing in the approximate direction of the S-O 2 bond.A combination of density functional and optimal control theory has been used by the authors to generate amplitude-and phase-modulated excitation pulses tailored specifically for the 33 S nuclei, based on one of several reported crystal structures.This allowed the authors to perform accurate determinations of the 33 S NMR interaction parameters at natural abundance and at a moderate magnetic field strength of 11.7 T. The 33 S NMR parameters were then used to assess the accuracy of various proposed crystal structures specified in Figure 23b,c.Very recently, Masuda et al. [9] performed experimental (Figure 12) and computational studies of polycrystalline 33 S-labeled taurine.The 33 S chemical shift anisotropy parameters agree with those reported by O'Dell and Ractliffe [59].It was concluded, however, that the orientations of the 33 S electric field gradient and chemical shift tensors cannot be determined accurately since even small changes in the local asymmetry of the -SO − 3 group could introduce significant inconsistencies among the computational methods and molecular structures used.O'Dell and Ratcliffe [59] reported the crystal structure for taurine shown in Figu 23a.It was found that the most shielded component of the chemical shift anisotropy t sor, σ 33 , was aligned within 3° of the S-C bond, with σ 11 pointing in the approximate dir tion of the S-O 2 bond, while the largest component of the EFG tensor, V 33 , was aligned ve anisotropy parameters agree with those reported by O'Dell and Ractliffe [59].It was cluded, however, that the orientations of the 33 S electric field gradient and chemical tensors cannot be determined accurately since even small changes in the local asymm of the -SO group could introduce significant inconsistencies among the computati methods and molecular structures used.Pallister and coauthors [60] applied a combination of solid-state NMR, first princ calculations, and single crystal XRD to relate solid-state 33 S NMR parameters obta from a series of anhydrous sulfates of the elements of groups I-III.It was shown tha experimental 33 S NMR spectra, exemplified in Figure 24, for Cs2SO4, and Rb2SO4, w dominated by the quadrupolar interactions.Magnetic shielding constants and quadr lar parameters for sulfur atoms were calculated using the plane wave pseudo-pote DFT.All calculated NMR parameters were found to be in very good agreement with experimental results, which helped in the assignment of the stationary spectra.Ind reported correlations between 33 S experimentally determined chemical shifts and ca lated isotropic shielding constants and quadrupolar coupling constants were chara ized by correlation coefficients R 2 of 0.93-0.95(Figure 25).Such a combined comp tional-experimental solid-state 33 S NMR approach could aid in the assessment and in pretation of the unique crystallographic data.Pallister and coauthors [60] applied a combination of solid-state NMR, first principles calculations, and single crystal XRD to relate solid-state 33 S NMR parameters obtained from a series of anhydrous sulfates of the elements of groups I-III.It was shown that the experimental 33 S NMR spectra, exemplified in Figure 24, for Cs 2 SO 4 , and Rb 2 SO 4, were dominated by the quadrupolar interactions.Magnetic shielding constants and quadrupolar parameters for sulfur atoms were calculated using the plane wave pseudo-potential DFT.All calculated NMR parameters were found to be in very good agreement with the experimental results, which helped in the assignment of the stationary spectra.Indeed, reported correlations between 33 S experimentally determined chemical shifts and calculated isotropic shielding constants and quadrupolar coupling constants were characterized by correlation coefficients R 2 of 0.93-0.95(Figure 25).Such a combined computationalexperimental solid-state 33 S NMR approach could aid in the assessment and interpretation of the unique crystallographic data.Halat and coauthors [34] reported ultra-wideline, high-field natural abundance solidstate 33 S NMR spectra of the Li-ion battery conversion electrode NbS3, emphasizing the fact that it was the first 33 S NMR study of a compound containing disulfide units.The large quadrupolar coupling parameters of about 31 MHz reported were consistent with the Halat and coauthors [34] reported ultra-wideline, high-field natural abundance solidstate 33 S NMR spectra of the Li-ion battery conversion electrode NbS 3 , emphasizing the fact that it was the first 33 S NMR study of a compound containing disulfide units.The large quadrupolar coupling parameters of about 31 MHz reported were consistent with the values obtained from the performed DFT calculations.As an illustration, several experimental and calculated at the DFT level 33 S NMR spectra of NbS 3 are presented in Figure 26.
Yamada and coworkers [45] performed experimental and theoretical investigations of the sulfur-33 EFG tensor of disulfide and trisulfide sulfur-sulfur bonds in the corresponding dibenzyl compounds.The orientations of the 33 S EFG tensor were obtained by quantum chemical calculations.It was found that the largest EFG tensor component, V ZZ , was approximately perpendicular to the molecular plane, while the smallest component, V XX , was approximately 41 • off the C-S bond.Extensive quantum chemical calculations were systematically performed by the authors to investigate the dependences of the 33 S EFG tensors on changes in torsion angles in disulfide and trisulfide bonds (the latter are shown in Figure 27), indicating that analysis of the ν Q and C Q values potentially makes it possible to assign the secondary structures of crosslinking in rubber.Yamada [44] reported four 33 S quadrupolar frequencies of the 33 S-enriched elemental sulfur, α-S 8 , which were observed in the range of 23.122-23.280MHz at 140 K and assigned based on the results of the quantum chemical calculations.The two-dimensional nutation echo 33 S NQR techniques were carried out for each quadrupolar frequency, providing the 33 S EFG tensor with the following information: the quadrupolar coupling constant and the asymmetry parameter.Quantum chemical calculations were also performed to complete the spectral assignment and to obtain the 33 S EFG tensor orientations with respect to the molecular frame.As shown in Figure 28, the nutation NQR spectrum of α-S 8 exhibits a powder pattern with three sharp singularities, denoted as ν1, ν2, and ν3 (ν1 < ν2 < ν3), and these frequencies can be used to obtain ν Q in a straightforward way.S 2 in dibenzyl trisulfide.The results for ν Q were given as differences from those of ϕ1 = ϕ2 = 0° in kHz, and gradient values are expressed by red arrows.Hydrogen, carbon, and sulfur are shown in white, grey, and yellow, respectively.Reproduced with minor editing privilege from Yamada et al. [45] with the permission of Elsevier, Amsterdam, Netherlands.Yamada [44] reported four 33 S quadrupolar frequencies of the 33 S-enriched elemental sulfur, α-S8, which were observed in the range of 23.122-23.280MHz at 140 K and assigned based on the results of the quantum chemical calculations.The two-dimensional nutation echo 33 S NQR techniques were carried out for each quadrupolar frequency, providing the 33 S EFG tensor with the following information: the quadrupolar coupling constant and the asymmetry parameter.Quantum chemical calculations were also performed to complete the spectral assignment and to obtain the 33 S EFG tensor orientations with respect to the molecular frame.As shown in Figure 28, the nutation NQR spectrum of α-S8 exhibits a powder pattern with three sharp singularities, denoted as ν1, ν2, and ν3 (ν1 < ν2 < ν3), and these frequencies can be used to obtain νQ in a straightforward way.Bellan and coauthors [39] reported 33 S solid-state NMR experiments at ultra-high fields and DNP experimental data coupled with DFT calculations, which allowed, for the Bellan and coauthors [39] reported 33 S solid-state NMR experiments at ultra-high fields and DNP experimental data coupled with DFT calculations, which allowed, for the first time, to propose a structural model of ZnS nanoplatelets in full agreement with the observed optical and conductive properties.This study represented a step toward the use of NMR spectroscopy coupled with DFT calculations for a better understanding of the structure-property relationship of the metal sulfide nanomaterials.
The most recent paper by Kupka and coauthors [61] described the crystal and molecular structures of three new thiosulfonates.Theoretical analysis of molecular structure and vibrational IR, Raman, and NMR spectra was carried out.Theoretical structures closely resemble their geometry in the solid state.A profound influence of the substituent effect of amino and acetamido groups on the SO 2 S moiety in the p-position of the phenyl group was derived from theoretically computed quantitative aromaticity indexes based on geometric, magnetic, and electronic criteria.The substituent effect in the studied molecules, leading to chinoid structures of the phenyl ring and shortening of the C Ar -S bonds, was clearly pronounced both in crystal and DFT-calculated geometries.In addition, the presence of the oxygen-lone electron pairs on one side of the phenyl group was found to provide different aromaticities above and below the ring plane.
Combination of NMR studies at various magnetic fields, various signal enhancement techniques, line shape analysis/simulation of experimental data, and first principles calculations resulted in several isotropic, δ iso , and nuclear quadrupole coupling constants C Q and n Q, which are compiled in Table 7.Chemical shifts of metal sulfides exhibited an extremely large chemical shift range of over 600 ppm (Figure 7), which was explained in terms of the crystalline ionicities and the effects of orbital overlap [1].DFT calculations by Laskowski and Blaha [62] showed that the variation of δ( 33 S) in sulfides is mainly related to the presence of metal d states and their variation in the energy position within the conduction bands.The sulfate chemical shifts exhibit a narrow range of ~80 ppm, which is rather similar to that in solution, but with a wider range of C Q values of 0.53 to 2.3 MHz (Table 7).C Q values increase significantly to 10.6 MHz in KHSO 4 , 15.9 MHz in K 2 S 2 O 8, and 16.2 MHz in K 2 S 2 O 7 .

Conclusions and Prospects for Future Research
From the present review, it becomes evident that the number of reports of 33 S NMR in solution and, to a lesser extent, in the solid state is extremely sparse.Nevertheless, several technical and methodological advances and the availability of elemental 33 S (99.8 atom %) as the starting material for isotope enrichment are expected to give a significant impetus to 33 S NMR, which are summarized below.
(1) Ultra-high-field instrumentation and high-sensitivity detection schemes will significantly enhance sensitivity and resolution in the case of: (i) small molecular-weight biological molecules with sulfur in a highly symmetric environment, which can be detected in enzymatic reaction products and in metabolomic studies [13].(ii) Ligands, with C Q ( 33 S) «10 MHz, bound to macromolecules and utilization, outside the extreme narrowing condition, of the m = 1/2 → m = −1/2 component, which is expected to result in significantly narrower resonances than the other component.Nevertheless, the prospect of recording meaningful NMR spectra for sulfur amino acid residues in proteins is rather poor.The use of 77 Se as a substitution for sulfur for 1 H detection in 77 Se NMR is, probably, the method of choice [30].(iii) Solid state since the secondorder quadrupolar line width of the m = 1/2 → m = −1/2 central transition decreases linearly with the magnetic field [36].In addition, significant sensitivity enhancement is expected with the use of selective polarization transfer between the four 33 S energy levels [37].(2) Spin-echo experiments of the broad band excitation of static solids and refocusing at several frequencies can be successfully used to map out line shapes resulting from sulfur sites with C Q ( 33 S) > 10 MHz.(3) Dynamic nuclear polarization (DNP) NMR would allow orders of magnitude sensitivity enhancement [39] and, thus, 33 S NMR studies at natural abundance within a reasonable experimental time.(4) The indirectly detected satellite transition via saturation of the proton reservoir (PROSPR) method and its variants [42,48] are expected to open new avenues of applications in investigating dynamic processes over a wide range of time scales.(5) Zero-field NMR (NQR) and frequency/field-swept NMR.Although this method may sound rather esoteric for ultra-high-field NMR spectroscopists, it should be emphasized that successful spectra were recorded using zero-field NMR of selectively enriched 33 S organosulfur compounds and models of cross-linked structures in rubber, with C Q values in the range of [42][43][44][45]63,64]. (6) The widespread availability of software and computational methods, the line-shape analysis and simulation of experimental data, and the great potentialities of ab initio calculations of NMR parameters will provide excellent means for structural and electronic information at the atomic level.
It should be emphasized, however, that for solid-state DNP-NMR experiments, specialized instrumentation is required, which is commercially available, or several components are necessary to upgrade more conventional wide-bore NMR instruments.Commercial zero-field NQR and frequency/field-swept NMR instruments are not widely spread and, in several cases, are available in specialized laboratories [45].Fortunately, the highly promising indirectly detected satellite transition via saturation of the proton reservoir (PROSPR) method and its variants [42,48] can be applied with conventional NMR instrumentation with modest hardware modifications at room temperature, It is hoped that the present review will encourage a wide range of researchers to utilize 33 S NMR spectroscopy as a powerful tool to provide structural, electronic, and dynamic information in a wide range of chemical, geological, and industrial applications.

Figure 4 .
Figure 4. Comparison of the 33 S NMR sensitivity measured for a 20 mM taurine in D2O solution.Acquisition parameters were: spectral width 130 ppm; acquisition time 0.1 s; preacquisition delay 6-10 µs; relaxation delay 0.05 s; number of scans 40,000 (the corresponding experimental time was 2 h).The NMR spectra were obtained: (a) using a conventional 5 mm broadband probe, T = 300 K; (b) with the 10 mm cryogenic probe with a room temperature rf switch and a preamplifier, T = 300 K; (c) using the 10 mm cryogenic probe with a cold rf switch and a cold preamplifier operated at 60 K.The sample temperature was 292 K. Reprinted with permission from[13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

Figure 4 .
Figure 4. Comparison of the 33 S NMR sensitivity measured for a 20 mM taurine in D 2 O solution.Acquisition parameters were: spectral width 130 ppm; acquisition time 0.1 s; preacquisition delay 6-10 µs; relaxation delay 0.05 s; number of scans 40,000 (the corresponding experimental time was 2 h).The NMR spectra were obtained: (a) using a conventional 5 mm broadband probe, T = 300 K; (b) with the 10 mm cryogenic probe with a room temperature rf switch and a preamplifier, T = 300 K; (c) using the 10 mm cryogenic probe with a cold rf switch and a cold preamplifier operated at 60 K.The sample temperature was 292 K. Reprinted with permission from[13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

Molecules 2024 , 43 Figure 5 .
Figure 5. Selected region of a heteronuclear33 S/19 F NMR correlation spectrum of gaseous SF6 at high pressure (approximately 20 atm).The 2D spectrum was obtained by the application of the refocused 33 S-19 F HMQC technique.Sixteen scans were collected for each TPPI dataset in 180 t1 increments.The maximum t1 and t2 times were 90 and 512 ms, respectively.A relaxation delay of 0.1 s was used.The data matrix containing 180 × 2048 complex points in t1 and t2 was zero-filled to 512 × 4096 complex points and apodized by a cosine function in both time domains prior to Fourier transformation.Reprinted with permission from[17].Copyright 2002, The American Institute of Physics, Melville, NY, USA.

Figure 5 .
Figure 5. Selected region of a heteronuclear33 S/19 F NMR correlation spectrum of gaseous SF 6 at high pressure (approximately 20 atm).The 2D spectrum was obtained by the application of the refocused 33 S-19 F HMQC technique.Sixteen scans were collected for each TPPI dataset in 180 t 1 increments.The maximum t 1 and t 2 times were 90 and 512 ms, respectively.A relaxation delay of 0.1 s was used.The data matrix containing 180 × 2048 complex points in t 1 and t 2 was zero-filled to 512 × 4096 complex points and apodized by a cosine function in both time domains prior to Fourier transformation.Reprinted with permission from[17].Copyright 2002, The American Institute of Physics, Melville, NY, USA.

Figure 7 .
Figure7.33 S NMR chemical shift ranges of some of representative sulfur functional groups of diamagnetic organic and inorganic compounds relative to saturated (NH4)2SO4 in D2O as reference calibrated at 0 ppm.

Figure 7 .
Figure 7. 33 S NMR chemical shift ranges of some of representative sulfur functional groups of diamagnetic organic and inorganic compounds relative to saturated (NH 4 ) 2 SO 4 in D 2 O as reference calibrated at 0 ppm.

Figure 8 .
Figure 8.(a) 33 S NMR spectrum of chondroitin sulfate A(ChS-A) in the absence of the enzym droitinase-ACII Arthro.(b) 33 S NMR spectra of chondroitin sulfate A with the enzyme; the ters listed are the incubation times of the enzyme catalyzing reaction.The NMR spectra tained with the use of a 33 S cryogenic probe, a room-temperature rf switch, and a room-tem preamplifier.Acquisition parameters: spectral width 130 ppm; acquisition time 0.1 s; preac delay 10 µs; and relaxation delay 0.01 s.Total number of scans: 400,000, and experimental h, 10 min.The sample temperature was in the range of 290-292 K. Reprinted with permiss [13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

Figure 8 .
Figure 8.(a) 33 S NMR spectrum of chondroitin sulfate A(ChS-A) in the absence of the enzyme chondroitinase-ACII Arthro.(b)33 S NMR spectra of chondroitin sulfate A with the enzyme; the parameters listed are the incubation times of the enzyme catalyzing reaction.The NMR spectra were obtained with the use of a33 S cryogenic probe, a room-temperature rf switch, and a room-temperature preamplifier.Acquisition parameters: spectral width 130 ppm; acquisition time 0.1 s; preacquisition delay 10 µs; and relaxation delay 0.01 s.Total number of scans: 400,000, and experimental time: 16 h, 10 min.The sample temperature was in the range of 290-292 K. Reprinted with permission from[13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.

Figure 9 .
Figure 9. 33 S NMR spectra of (a) mantle edge, (b) midgut, and (c) adductor muscl (d) of sea water.The spectra were obtained with the use of the 33 S cryogenic p switch and a cold preamplifier (60 K).The acquisition parameters were the sa

Figure 9 .
Figure9.33 S NMR spectra of (a) mantle edge, (b) midgut, and (c) adductor muscles of a scallop, and (d) of sea water.The spectra were obtained with the use of the33 S cryogenic probe with a cold rf switch and a cold preamplifier (60 K).The acquisition parameters were the same as in Figure8.400,000 scans were recorded, and the experimental time was 16 h 10 min.Sample temperature: 291-292 K. Reprinted with permission from[13].Copyright 2010, The American Institute of Physics, Melville, NY, USA.
Molecules 2024, 29, x FOR PEER REVIEW 17 of 43 (ii) Magic-angle spinning observation of the central transition: effects of Bo and population transfer.(iii) Dynamic nuclear polarization (DNP) in NMR.

Figure 11 .
Figure 11.Schematic diagram of the energy levels of a spin I = 3/2 nucleus in an external magnetic field B0 due to Zeeman interactions with additional shifts originating from the first-and secondorder quadrupole interactions.Reprinted with permission from [32].Copyright 2015, The American Physical Society, Washington, DC, USA.

Figure 11 .
Figure 11.Schematic diagram of the energy levels of a spin I = 3/2 nucleus in an external magnetic field B 0 due to Zeeman interactions with additional shifts originating from the first-and second-order quadrupole interactions.Reprinted with permission from [32].Copyright 2015, The American Physical Society, Washington, DC, USA.
S NMR spectra in the solid state: (i) Static spectra: ultra-wideline Carr Purcell Meiboom Gill (CPMG) technique.(ii) Magic-angle spinning observation of the central transition: effects of B o and population transfer.(iii) Dynamic nuclear polarization (DNP) in NMR.

Figure 14 .
Figure 14.Natural abundance33 S MAS NMR spectra (ν r = 6 kHz) of (NH 4 ) 2 MoS 4 displayed on an absolute intensity scale for (a) without polarization transfer and (b) with hyperbolic secant (HS) polarization transfer.Both spectra were observed using single-pulse excitation and identical experimental conditions, i.e., 48,000 scans, 1 s relaxation delay, and 13.3 h.(c) Simulation based on the NMR spectrum in (b).Adopted with permission from[37].Copyright 2008, Elsevier, Inc., Amsterdam, Netherlands.The chemical shift range has been corrected relative to saturated (NH 4 ) 2 SO 4 in D 2 O (0 ppm), according to IUPAC recommendation[5].

Figure 15 .
Figure 15.(A) Experimental (black) and simulated (red) conventional 33 S direct excitation NMR spectra of ZnS•DDA NPls acquired at 18.8 T (top) and 35.2 T (bottom).The spectra are the FT of the sum of QCMPG echoes.(B) Experimental (black) and simulated (red) DNP-enhanced 1 H → 33 S D-RINEPT variable offset cumulative spectrum of ZnS•DDA NPls impregnated with 13 mM TEKPol solution in TCE acquired at 9.4 T and 105 K with νR = 13.89kHz.The spectrum is the sum of four sub-spectra obtained by the FT of the sum of QCMPG echoes.Reprinted with permission from [39].Copyright 2023, The American Chemical Society, Washington, DC, USA.

Figure 15 .
Figure 15.(A) Experimental (black) and simulated (red) conventional 33 S direct excitation NMR spectra of ZnS•DDA NPls acquired at 18.8 T (top) and 35.2 T (bottom).The spectra are the FT of the sum of QCMPG echoes.(B) Experimental (black) and simulated (red) DNP-enhanced 1 H → 33 S D-RINEPT variable offset cumulative spectrum of ZnS•DDA NPls impregnated with 13 mM TEKPol solution in TCE acquired at 9.4 T and 105 K with ν R = 13.89kHz.The spectrum is the sum of four sub-spectra obtained by the FT of the sum of QCMPG echoes.Reprinted with permission from [39].Copyright 2023, The American Chemical Society, Washington, DC, USA.

Figure 18 .
Figure 18.(a) Variable-temperature single-crystal 33 S PROSPR measurements of the paraelectric to ferroelectric phase transition of ammonium sulfate; significant changes in the ST are lost in the CT spectra.(b) Temperature-dependence is shown by the ST and CT 33 S resonance frequencies in these experiments.The structures shown in between (a) and (b) depict the changes presumed for the ammonium and sulfate (red/yellow balls) groups of (NH4)2SO4, upon going from the paraelectric phase

Figure 18 .
Figure 18.(a) Variable-temperature single-crystal 33 S PROSPR measurements of the paraelectric to ferroelectric phase transition of ammonium sulfate; significant changes in the ST are lost in the CT spectra.(b) Temperature-dependence is shown by the ST and CT 33 S resonance frequencies in these experiments.The structures shown in between (a) and (b) depict the changes presumed for the ammonium and sulfate (red/yellow balls) groups of (NH 4 ) 2 SO 4 , upon going from the paraelectric phase (PE, lower inset) to the ferroelectic phase (FE, upper inset).Reprinted with permission from [48].Copyright 2023, Elsevier, Inc., Amsterdam, Netherlands.

Figure 19 .
Figure19.33 S nuclear isotropic shielding constants of 2-thiouracil calculated at the (A)-B3LYP/augcc-pVXZ and B3LYP/aug-cc-pCVXZ levels of theory, and (B)-using the LDBS approach, where only the sulfur atom was described using either the aug-cc-pVXZ or aug-cc-pCVXZ while the 6-31G* basis set was applied on H, C, N, and O atoms[51].

Figure 20 .
Figure 20.Calculated versus observed sulfur absolute shieldings (ppm) for the scaled DFT (solid circles) and EMPI (open circles) methods.Reproduced from Chesnut and Quin [53] with the per mission of Wiley, Chichester, West Sussex, UK.

Figure 20 .
Figure 20.Calculated versus observed sulfur absolute shieldings (ppm) for the scaled DFT (solid circles) and EMPI (open circles) methods.Reproduced from Chesnut and Quin [53] with the permission of Wiley, Chichester, West Sussex, UK.

Molecules 2024 ,Figure 22 .
Figure 22.Top: 33 S QCPMG spectra of K2S2O7 (top) and K2S2O8 (bottom) at 21.14 T. (a,c) Spectra h been obtained by coadding 14 equally offset subspectra.Each subspectrum is the result of 2000 cumulations with a 10 s delay.The upper traces (b,d) are the WSolids simulations of the spec using a single site and a model of the central transition of spin 3/2.The inset demonstrates the culated orientation of the EFG tensor.Sulfur and oxygen are shown in yellow and red, respective Reproduced from Moudrakovski et al. [58] with the permission of the American Chemical Socie Washington, DC, USA.

Figure 22 .
Figure 22.Top: 33 S QCPMG spectra of K 2 S 2 O 7 (top) and K 2 S 2 O 8 (bottom) at 21.14 T. (a,c) Spectra have been obtained by coadding 14 equally offset subspectra.Each subspectrum is the result of 2000 accumulations with a 10 s delay.The upper traces (b,d) are the WSolids simulations of the spectra using a single site and a model of the central transition of spin 3/2.The inset demonstrates the calculated orientation of the EFG tensor.Sulfur and oxygen are shown in yellow and red, respectively.Reproduced from Moudrakovski et al. [58] with the permission of the American Chemical Society, Washington, DC, USA.

Figure 23 .
Figure 23.(a) Electric field gradient and chemical shift anisotropy tensor orientations in taurin the 33 S quadrupolar interaction; (c) the 33 S chemical shift anisotropy tensor orientations.The n bers n = 1-10 correspond to the CCSD code of the structure used (TAURINn), reproduced with nor editing privilege from O'Dell and Ratcliffe[59] with the permission of the American Chem Society, Washington, DC, USA.

Figure 23 .
Figure 23.(a) Electric field gradient and chemical shift anisotropy tensor orientations in taurine; (b) the 33 S quadrupolar interaction; (c) the 33 S chemical shift anisotropy tensor orientations.The numbers n = 1-10 correspond to the CCSD code of the structure used (TAURINn), reproduced with minor editing privilege from O'Dell and Ratcliffe[59] with the permission of the American Chemical Society, Washington, DC, USA.

Figure 24 .
Figure 24.Experimental 33 S stationary Hahn Echo spectra at 21.1 T (69.1 MHz) of Cs2SO4 (A) and Rb2SO4 (B).(A)-Experimental 5 kHz MAS Bloch Decay spectrum, (A′)-Simulation.(A′,B′) are corresponding simulation accounting for the EFG and CSA interactions.(C)-Representative portion of the Rb2SO4 unit cell showing the calculated orientations for the principal components of the EFG and CSA tensors.Sulfur, oxygen, and alkali metal are shown in yellow, red, and purple, respectively.The mirror plane present through sulfur is shown in yellow.Reproduced from Pallister et al.[60] with the permission of the Royal Society of Chemistry, London, UK.The chemical shift range reported relative to CS2 (0 ppm) has not been corrected relative to saturated (NH4)2SO4 in D2O (0 ppm), which is recommended by IUPAC[5].

Figure 24 . 43 Figure 25 .
Figure 24.Experimental 33 S stationary Hahn Echo spectra at 21.1 T (69.1 MHz) of Cs 2 SO 4 (A) and Rb 2 SO 4 (B).(A)-Experimental 5 kHz MAS Bloch Decay spectrum, (A ′ )-Simulation.(A ′ ,B ′ ) are corresponding simulation accounting for the EFG and CSA interactions.(C)-Representative portion of the Rb 2 SO 4 unit cell showing the calculated orientations for the principal components of the EFG and CSA tensors.Sulfur, oxygen, and alkali metal are shown in yellow, red, and purple, respectively.The mirror plane present through sulfur is shown in yellow.Reproduced from Pallister et al. [60] with the permission of the Royal Society of Chemistry, London, UK.The chemical shift range reported relative to CS 2 (0 ppm) has not been corrected relative to saturated (NH 4 ) 2 SO 4 in D 2 O (0 ppm), which is recommended by IUPAC [5].Molecules 2024, 29, x FOR PEER REVIEW 33 of 43

Figure 25 .
Figure 25.(a) Correlation between 33 S experimentally determined chemical shift and calculated isotropic shielding constants for all known crystal structures of anhydrous sulfates.(b) Correlation between 33 S experimentally determined quadrupolar coupling constant, C Q , and the calculated quadrupolar coupling constant, C Q calc for the sulfate compounds.The red circles represent calculations for all structures, including those after the geometry optimization.The solid black circles indicate the structures that provided the best agreement with the calculated EFG.Reproduced with minor editing privilege from Pallister et al. [60] with the permission of the Royal Society of Chemistry, London, UK.The chemical shifts reported relative to CS2 (0 ppm) have not been corrected relative to saturated (NH4)2SO4 in D2O (0 ppm), which is recommended by IUPAC [5].

Figure 25 .
Figure 25.(a) Correlation between 33 S experimentally determined chemical shift and calculated isotropic shielding constants for all known crystal structures of anhydrous sulfates.(b) Correlation between 33 S experimentally determined quadrupolar coupling constant, C Q , and the calculated quadrupolar coupling constant, C Q calc for the sulfate compounds.The red circles represent calculations for all structures, including those after the geometry optimization.The solid black circles indicate the structures that provided the best agreement with the calculated EFG.Reproduced with minor editing privilege from Pallister et al. [60] with the permission of the Royal Society of Chemistry, London, UK.The chemical shifts reported relative to CS 2 (0 ppm) have not been corrected relative to saturated (NH 4 ) 2 SO 4 in D 2 O (0 ppm), which is recommended by IUPAC [5].

Figure 27 .
Figure 27.Contour plots of calculated ν Q versus the two dihedral angles, ϕ1 and ϕ2, for (a) S 1 and (b)

Figure 28 .
Figure 28.A simulated nutation echo NQR spectrum, which exhibits the three sharp singularities denoted as ν1, ν2, and ν3.The molecular structure of α-S8, determined by X-ray diffraction, is shown on top.Reproduced with minor editing privileges from Yamada [44] with the permission of Elsevier, Amsterdam, Netherlands.

Figure 28 .
Figure 28.A simulated nutation echo NQR spectrum, which exhibits the three sharp singularities denoted as ν1, ν2, and ν3.The molecular structure of α-S 8 , determined by X-ray diffraction, is shown on top.Reproduced with minor editing privileges from Yamada [44] with the permission of Elsevier, Amsterdam, Netherlands.

Table 2 .
Experimental 33 S NMR chemical shifts and line widths of the representative sulfides, sulfoxides, and sulfones a .

Table 2 .
Experimental 33 S NMR chemical shifts and line widths of the representative sulfides, sulfoxides, and sulfones a .

Table 2 .
Experimental 33 S NMR chemical shifts and line widths of the representative sulfides, sulfoxides, and sulfones a .

Table 2 .
Experimental 33 S NMR chemical shifts and line widths of the representative sulfides, sulfoxides, and sulfones a .

Table 3 .
Experimental 33 S NMR chemical shifts and line widths of several representative sulfones.

Table 3 .
Experimental 33 S NMR chemical shifts and line widths of several representative sulfones.
a Chemical shifts are given in the SO 4 2-and CS 2 scales (the latter are given in parenthesis).

Table 3 .
Experimental 33S NMR chemical shifts and line widths of several representative sulfones.Cmpd.

33 S NMR Chemical Shift, ppm Line Width, Hz SO 4 2− Scale CS 2 Scale
•12H 2 O at 17.6 T relative to that of 4.7 T [36].

Table 4 .
[46]Quadrupole coupling (C Q and n Q ), chemical shift anisotropy parameters (δ ani and η ani ) and δ iso for [(C 2 H 5 ) 4 N][ReS 4 ] determined from natural abundance WURST polarization transferenhanced33S MAS and 33 S static QCPMG NMR spectra.aAdopted with permission from[46].Copyright 2010, Elsevier, Inc.The optimum parameter set is shown in entry II.In the simulations for the S1 and S2 sites, the intensity ratio used was S1:S2 = 1:3, in accordance with the crystal structure for [(C 2 H 5 ) 4 N][ReS 4 ].Due to the three-fold symmetry axis for S1, no error limits are given for n Q .The error limits for the C Q values for both the S1 and S2 sites are within ±0.05 MHz.These error limits apply for all C Q and n Q values in Table1, entries I-IV.b In parenthesis are the original chemical shifts reported relative to CS 2 (0 ppm). a The optimum parameter set is shown in entry II.In the simulations for the S1 and S2 sites, the intensity ratio used was S1:S2 = 1:3, in accordance with the crystal structure for [(C2H5)4N][ReS4].Due to the three-fold symmetry axis for S1, no error limits are given for  .The error limits for the  values for both the S1 and S2 sites are within ±0.05 MHz.These error limits apply for all  and  values in Table1, entries I-IV.b In parenthesis are the original chemical shifts reported relative a

Table 7 .
Isotropic33S chemical shifts, δ iso , and nuclear quadrupole coupling constants C Q and n Q in the solid state (in brackets are the chemical shifts relative to CS 2 at 0 ppm).